TECHNOLOGY, ENTREPRENEURSHIP, AND INEQUALITY

Alfonso Gambardella Sant’Anna School of Advanced Studies, Pisa, Italy [email protected] David Ulph University College London, London, UK [email protected]

February 2002

We would like to thank David Encaoua, Fernando Galindo-Rueda, Cecilia GarciaPeñalosa, Donatella Gatti, Omer Moav, Thomas Moutos, Fabio Pammolli, Mauro Sylos Labini, Davide Ticchi, and Salvatore Torrisi for helpful comments and suggestions. They are not responsible for errors or omissions. Financial support from the DGXIITSER project Growth, Inequality and Training (Contract N.SOE2-CT98-3073) and the CNRS Programme Les Enjeux Economique de l’Innovation are gratefully acknowledged.

Abstract This paper links the rise of new industries populated by skill-intensive companies, and the divergence in labour incomes between skills. Our model explains inequality by the fact that as the skilled workers move towards new Silicon-Valley type firms, the reduced complementarity between skilled and unskilled workers in the traditional manufacturing sectors lessens the productivity of the latter. In addition, knowledge externalities in the modern sector produce two equilibria in which either the modern sector dominates (and inequality between skills is high), or manufacturing dominates (inequality is low). We provide suggestive evidence consistent with our model.

Keywords: Technology, Entrepreneurship, Wage Inequality JEL: J32, L22

1. INTRODUCTION Apart from a technological revolution, the information technology (IT) industries have encouraged new managerial practices and new business models. In particular, they have given a great impetus to decentralised patterns of production and invention hinging on smaller technology-based companies and start-ups, entrepreneurship, clusters of firms, along with a focus on new design, innovation, and skilled-labour intensive activities. (See Langlois and Robertson, 1992, and Baldwin and Clark, 1997. See also Hall and Ham, 2001, and Arora, Fosfuri, and Gambardella, 2001.) Moreover, the IT model, which is often symbolised by the Silicon Valley (Saxenian, 1994), has spread not only to other industries, but also across regions, including non G-8 countries like in the case of Israel, Ireland, or the Indian software industry. (See Arora et al., 2001, and Arora, Gambardella, and Torrisi, 2001.) Given the innovation performance of these models in recent years, one is tempted to argue, as it has been done for instance by the popular press for some time, that they are inherently superior forms of organising firms and industries compared to the large integrated firms of Chandlerian memory (Chandler, 1990). A central tenet of this paper is that this is the wrong way of posing the question. For example, Levinthal and March (1993) have suggested that the larger organisations are better at “exploiting” innovations, while smaller, flexible firms are better at “exploring” new avenues. This is is not necessary either, as there are instances in which the two organisational models carry out very similar production and innovation activities (e.g. Chesbrough, 1999). Even in the so-called “new economy” − a flamboyant concept that in many respects overlaps with that of IT industries − some IT segments are populated by clusters of smaller firms, while in others classical larger firms dominate. Of course, the two

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models influence each others. Today, many large firms are becoming more “entrepreneurial” (e.g. Chesbrough, 2000), while many technology-based smaller firms have realised that good management, some degree of integration, and a fairly tight organisational structure, are crucial for longer run profitability. Nonetheless, they do remain fairly distinct organisational set-ups. This paper develops a model which links the rise of these new industries with the growing inequality of earnings between skilled and unskilled workers that is observed in some modern economies. Several authors have documented the growth in inequality (e.g. Gottschalk, 1997; Gottschalk and Smeeding, 1997; Aghion, Caroli, GarciaPeñalosa, 1999), and an important stream of the literature has emphasised the effects produced by skill-biased technical change on the demand for skilled workers (e.g., Goldman and Katz, 1998; Berman, Bound and Machin, 1998; Machin and Van Reenen, 1998; Bresnahan, 1999; Berman and Machin, 2000; Caroli and Van Reenen, 2000; Brynjolfsson, Bresnahan, and Hitt, 2001). Acemoglu (2001) has provided an extensive survey of the relationships between technical change and skill premia, and highlighted the main open questions. First, he notes that little has been done to understand the combined effects, on the wage structure, of technical change and changes in “the way in which firms are organised, or perhaps in the way that firms and workers match” (ib. 9). Second, a largely open question is why the growth of inequality is less pronounced in some countries compared to others. This certainly depends on market forces (e.g. supply of skills) and institutional differences, as argued for instance by Gottschalk and Smeeding (1997). However, it is intriguing that the more pronounced inequality is in the Anglo-Saxon world, and in regions with similar institutional characteristics, which have favoured the rise of high-tech

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entrepreneurship and more decentralised modes of organising production. Less pronounced inequalities are in Germany or Japan, wherein the classical large firms still play a predominate role. Gottschalk and Smeeding (1997), along with others (e.g. Casavola, Gavosto, Sestito, 1996), argue that inequality is lower in countries with centralised wage setting mechanisms. But such centralised mechanisms, and the related unionisation of workers, are correlated with the presence of the large firms, while economies that exhibit start-ups and a fair degree of entrepreneurship depend on more decentralised processes for determining people’s earnings. While we do not dispute that institutional factors are important, the scope of this paper is to highlight the role of the new organisational models, which has not been emphasised by this literature. There is a third issue which is only indirectly addressed by Acemoglu. There can be two forms of inequality: Both the salaries of the skilled workers and the wages of the unskilled workers rise, but the former rise faster than the latter; or the former rise, and the latter decline. This point was also noted by Feldstein (1998) who argued that it is the second type of inequality that ought raise our concerns about “poverty”, while the first type of inequality even implies a Pareto-superior situation. The inequality observed in the US since the 1970s is of the second type, viz. the wages of the unskilled workers have systematically declined. In continental Europe one observes a modest growth in inequality, and whatever inequality is observed does not entail any sizable decline in the real wages of the workers with lower incomes. The model developed in this paper touches upon all these three issues. First, it associates inequality with the new business models that have emerged in the high-tech industries. New firms in these industries are highly skilled-labour intensive. By contrast, the classical Chandlerian firms employ both skilled and unskilled people. For

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example, they employ both skilled managers or R&D personnel and manufacturing workers; or marketing strategists and mere salesmen. This is a natural consequence of their integrated structure, which entails that they conduct more strategic and creative activities along with more routinary ones like final production, sales, etc.. Moreover, in these firms, skilled and unskilled workers are complementary. For example, a higher number of skilled managers is likely to induce more extensive investments in advanced manufacturing technologies which increases the productivity of the less skilled workers. Similarly, clever marketing strategists design effective procedures for enhancing the ability of their salesmen to sell their products. The model developed in this paper explains inequality by the fact that, as opportunities in the new sectors grow, and skilled workers move away from manufacturing to set-up their own Silicon-Valley type hightech companies, the reduced supply of skilled workers in manufacturing reduces the productivity of the unskilled workers. In this respect, our model has some similarity with the story of the segregation of worked by skills found in Kremer and Maskin (1999), and Acemoglu (1999). Our focus however is not on deriving the segregation of workers endogenously, as they do. We simply assume that there are firms with different degrees of skill intensity, and justify this assumption by the increasing importance of new types of firms and business models in industries like IT or biotechnology. Moreover, while they look at the role played by search costs and labour market frictions which may prevent from finding out ex-ante with certainty whether a worker is skilled or not, our goal in this paper is to focus on one key feature of the main asset employed by the new firms, notably that knowledge or technology can be re-used for other purposes. Knowledge spillovers are common for instance in the software industry, where codes or programmes are normally re-used by

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others in other programmes, or in semiconductors, where new designs often build on existing ones, or in biotechnology, where basic scientific knowledge is never reproduced totally from scratch by any new firm. These externalities are crucial for obtaining two equilibria in our model − one in which the new sector does not arise, and another one in which the skilled workers split between new and “old” companies. We also find that while in terms of average income neither equilibrium is unambiguously superior to the other, they exhibit very different patterns of inequality. In the latter the salary of the skilled workers is higher than in the former, while the wages of the unskilled workers are lower because of the reduced complementarity with the skilled workers. We draw two conclusions from this. First, the underlying complementarity between skilled and unskilled labour in the classical manufacturing industries has been a notable shield against inequality across skills. Second, our multiple equilibria story can explain inter-country differences without appealing to differences in the impact of technological shocks, which today appear to be largely common across them, especially in the advanced world. Finally, our model can explain the two types of inequality mentioned earlier. In the equilibrium with no modern sector, any increase in the skill-bias technical change parameter implies an increase in the salaries of the skilled workers. The wages of the unskilled workers also rise because of the complementarity with the efficiency units of skilled workers. However, the wages of the unskilled workers increase less strongly than those of the skilled people. By contrast, in the equilibrium with the new industries, increases in the productivity of the skilled workers in the new sectors lower the wages of the unskilled workers. Moreover, the higher the productivity of the traditional industries the lower the advantage (in terms of average income of the economy) of the

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equilibrium with the new sector. This is suggestive of why new IT business models, high-tech entrepreneurship, and the like, have emerged in regions without a substantial industrial tradition. Put simply, German skilled workers, with potential employment in companies like BMW, Bayer or Mercedes, have higher opportunity costs of setting up their own firms vis-à-vis Indian or Israeli engineers. The next section presents the basic structure of the model. Section 3 shows the equilibrium allocations. Section 4 presents the comparative static results, and the implications for inequality. Section 5 discusses the implications for the average income of the economy. Section 6 provides suggestive evidence consistent with our model. Section 7 concludes. The Appendix illustrates some technicalities not shown in the text.

2. STRUCTURE OF THE MODEL 2.1 The Economy In this economy the population of workers is normalised to 1. There are K skilled and 1-K unskilled workers. There are two sectors, which we label traditional and modern. The unskilled workers can work only in the traditional sector, while the skilled workers can work in both. In the modern sector the skilled workers can operate as entrepreneurs, setting up the firms, or as employees of the firms. Figure 1 describes the sequence of allocations. First, people allocate between skilled and unskilled workers. We do not model this allocation, and take the supply of the two types of workers as fixed. No additional insight would be produced if we modeled the supply of skills as well. The unskilled workers obtain a wage w. The skilled workers have to decide whether to work in the traditional or in the modern sector. Suppose that H1 , 0 ≤ H1 ≤ K, of the skilled workers work in the traditional

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sector, while H2 = K – H1 work in the modern sector. The salary of the skilled workes in the traditional sector is r1 . Of the H2 workers in the modern sector, N become entrepreneurs. There is a probability q, 0 ≤ q ≤ 1, that the firm is profitable. 1 The entrepreneurs obtain profits π > 0 with probability q, and zero with probability 1-q. The remaining H2 -N skilled workers are employed by the successful firms in the modern sector, where they earn r2 > 0.2 [FIGURE 1 ABOUT HERE] Finally, the individuals in this economy have utility function u ( y ) =

1 y 1− ρ 1− ρ

for their income y, where ρ, 0 ≤ ρ < 1 , is the coefficient of relative risk aversion.

2.2 The Traditional Sector Total output in the traditional sector is given by the production function σ

σ −1 σ −1 σ −1   Y = (θ ⋅ H 1 ) σ + (1 − K ) σ  , where σ > 0 is the elasticity of substitution between  

skilled and unskilled workers, and θ > 0 measures the productivity of skilled workers. We normalise the price of output to 1. Define h ≡

H1 K , 0 ≤ h ≤ 1 , and k ≡ . Profit K 1− K

maximisation implies σ −1

r1 = θ

σ

1

σ −1 σ −1  σσ−1 −  σ θ + ( hk )    

(1)

1

We assume that this probability is common across all entrepreneurs. This is therefore a feature of the economy rather than of the individuals. 2

We assume that if their ideas fail, the entrepreneures cannot be re-employed by the successful firms as skilled workers. This is necessary to avoid that they be fully insured.

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1

σ −1  σ −1  σ −1 w = θ σ ⋅ ( hk ) σ + 1  

(2)

σ −1 1 − r1 = θ σ ( hk ) σ w

(3)

and so

It follows from (3) that if we want that skill-biased technical progress − which we have parameterised by increases in θ − increase the ratio of skilled to unskilled wages, it is necessary that σ > 1. From now on, we will make this assumption. The intuition is that a rise in θ has two effects. First, it reduces the number of skilled relative to unskilled workers needed to produce any given output; second, it lowers the relative price of efficient skilled labour, and so it induces the firm to increase the demand for skilled relative to unskilled workers. Only if the elasticity of substitution is greater than 1 the second effect dominates leading to an overall increase in the demand for skilled relative to unskilled workers, and therefore to increases in their relative price. 3 From (1), also notice that: i)

r1 is a decreasing function of h and k

ii)

as h →0, r1 →∞ σ −1

1

σ −1 σ −1  σσ−1 −  σ θ + k >0    

iii)

as h →1, r1 → r 1 ≡ θ

iv)

with σ > 1, r1 is increasing in θ

v)

r 1 is also increasing in θ and decreasing in k.

3

σ

As noted by Acemoglu (2001), empirical studies have estimated σ to be be between 1 and 2.

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Similarly, from (2), w is a strictly increasing function of θ⋅h. This does not depend on the assumption that σ > 1. The intuition is that an increase in θ⋅h makes unskilled labour relatively more scarce and so it raises its price.

2.3 The Modern Sector In the modern sector, if an idea is successful the company will face a demand curve p = d⋅x -ε, where p is the price of the good, x is the quantity of output, d > 0 is a demand parameter, and ε, 0 < ε < 1, is the inverse price elasticity of demand. To produce the good, the firm will have to employ c > 0 skilled workers per-unit of output. For the moment c is taken as given. Output will be chosen to maximise profits π = d⋅x 1-ε c⋅r2 ⋅x. This implies 1 ε

1 1 −ε 1−ε c ⋅ r2  d (1 − ε )  ε  ; π = ε ⋅ (1 − ε) ε ⋅ d ⋅ (c ⋅ r2 )− ε p= ; x =  1− ε  c ⋅ r2 

(4)

To be indifferent between working as an entrepreneur or as a skilled employee, the expected utility of the entrepreneurs must equate the utility of the certain income r2 , 1

viz. q⋅u(π) + (1-q)⋅u(0) = u(r2 ), which implies q 1− ρ ⋅ π = r2 . By using the expression for π in (4), one obtains ε

r2 = q 1− ρ ⋅ εε ⋅ (1 − ε )1− ε ⋅ d ⋅ c −(1−ε )

(5)

Equation (5) is one equilibrium condition that must hold to leave the skilled workers indifferent between becoming entrepreneurs or salaried workers. The other equilibrium condition is that the supply of salaried workers must equal demand, i.e. N⋅q⋅c⋅x = H2 – N. Substitute x from (4), and obtain

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1−ε 1 1 1  −  N ⋅ 1 + q ⋅ c ε ⋅ d ε ⋅ (1 − ε )ε ⋅ r2 ε  = H 2  

(6)

Then, substitute r2 from (5) into (6). This yields N = ϕ ⋅ H2   1− ε where ϕ ≡ 1 + ρ  1− ρ  ε⋅ q

    

(7)

−1

is the fraction of skilled workers in the modern sector who

become entrepreneurs. Notice that this fraction is independent of c or d. It is instead: i)

increasing in ε: the more inelastic is demand the great the amount of profit to be made from setting up a company;

ii)

increasing in q: the greater the probability of being a successful entrepreneur the more skilled people will choose to do so;

iii)

decreasing in ρ: the more risk averse are the skilled workers, the fewer will choose to become entrepreneurs. To complete our analysis of the modern sector, we introduce our assumption

about knowledge spillovers. Firms draw on other firms for their ideas, so if there are no other firms in the sector it is impossible for one firm to be successful on its own. The more firms there are the better are the ideas that any one firm can come up with. To capture this we assume that c = χ⋅N-γ

(8)

where χ > 0 is a parameter that scales the skilled labour requirements in the modern sector and it is therefore inversely related to the skilled worker productivity in this

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sector, while γ > 0 is a parameter that controls for the extent of the spillovers. 4 Substitute (7) and (8) into (5), and use the fact that H 2 =

k ⋅ (1 − h ) . We 1+ k

obtain γ (1−ε )

k  r2 = µ ⋅    1+ k  where µ ≡ q

ε 1− ρ

(1 − h) γ (1−ε )

(9)

⋅ ε ε ⋅ (1 − ε)1−ε ⋅ d ⋅ χ −(1−ε ) ⋅ ϕγ (1 −ε ) . The parameter µ is then a single

parameter that captures all the factors that make the modern sector successful, and hence raise the productivity of the skilled workers in this sector. These are: i)

higher probability of discovering viable ideas – i.e. higher q;

ii)

higher demand for the output of the modern sector – i.e. higher d;

iii)

greater productivity of the skilled workers in the modern sector – i.e. lower χ;

iv)

greater willingness to bear risks – i.e. lower degree of risk aversion, ρ. Since γ > 0, it follows from (9) that r2 is a strictly decreasing function of h, and it

k  increases with k. Moreover, as h →0 then r2 → µ ⋅   1+ k 

γ (1−ε )

≡ r2 > 0 , while as h→

1 then r2 →0. Notice also that r2 is increasing both in µ and k.

We could generalise this to have c = χ⋅(N⋅q β) -γ where β, 0 ≤ β ≤ 1, is a parameter that controls the extent to which the spillovers come from active rather than inactive firms. But this more general specification would add no additional insights. 4

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3. EQUILIBRIUM ALLOCATIONS To determine the equilibrium allocation h of this economy, we study the intersections of the two functions r1 and r2 given by (1) and (9). The skilled workers will move to whichever sector pays the highest salary. We can analyse this graphically. As noted, the curve for r1 decreases with h, shifts downward with k, reaches its minimum r 1 at h = 1, and goes to ∞ as h →0. It is also not difficult to show that, for 0≤ h≤ 1, r1 decreases with h at an increasing rate, i.e.

∂ 2 r1 > 0 . The r2 -curve is also ∂h 2

strictly decreasing in h; it increases with µ and k; it is equal to zero for h = 1, and it reaches its maximum r2 at h = 0. We distinguish between two cases: 1) the r2 -curve intersects the r1 -curve; 2) the r2 -curve lies entirely below the r1 -curve. n Case 1: The r2 -curve intersects the r1 -curve The situation is depicted in Figure 2. The two conditions r2 < ∞ and r 1 > 0 , along with r2 →0 as h→1, and r1 →∞ as h→0, ensure that if the r2 -curve intersects the r1 -curve from below to the left of h = 1, it will also intersect it from above to the right of h = 0, as depicted in Figure 2. 5 We then have the following claim. [FIGURE 2 ABOUT HERE] Claim The economy depicted in Figure 2 has two stable equilibria:

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∂2r 2 < 0 . This is not necessary. The two conditions In Figure 2 we have depicted the r2 -curve as if 2 ∂h

r2 < ∞ and r 1 > 0 are enough to ensure the two intersections shown in the Figure.

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i)

the point labeled with A in the Figure, in which all the workers are employed in the traditional sector − i.e. h = 1. (We will call this the A-equilibrium.)

ii)

the point labeled with B in the Figure, a mixed equilibrium in which a small number of skilled workers are employed in the traditional sector, and the rest is employed in the modern sector − i.e. h < 1. (We will call this the Bequilibrium.)

Also, the salary of the skilled workers in the B-equilibrium is higher than the salary of the skilled workers in the A-equilibrium. Proof Point A is a stable equilibrium. This is because in A there is no incentive for any individual skilled worker to move to the modern sector, as r2 would remain below r1 . Point B is also a stable equilibrium. Suppose that an individual worker deviates by moving from the modern to the traditional sector. Since in B

∂r1 ∂r2 < , then the ∂h ∂h

implied increase in h would produce r1 < r2 . Hence, there are no incentives to deviate. Similarly, if the skilled worker moved from the traditional to the modern sector, then ∂r1 ∂r2 < would imply r2 < r1 . Finally, it is apparent from Figure 2 that the ∂h ∂h equilibrium salary r is higher in the B-equilibrium vis-à-vis the A-equilibrium. QED On comparing the A- and B-equilibrium, note that if the economy is in the Aequilibrium, some co-ordination is needed for the B-equilibrium to arise. A group of skilled workers has to move in a co-ordinated fashion to the modern sector so that h drops from 1 to just below h C in Figure 2. It is easy to see from the Figure that in this case r2 > r1 , and other skilled workers will move to the modern sector till the B-

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equilibrium is reached. The intuition is straight forward. The externalities in the use of knowledge or technology imply that a critical mass of activities in the modern sector is needed to make it viable given the alternative opportunities in the traditional sector. In Figure 3 we look at the comparative statics results produced by changes in µ, θ, and k. As µ increases, the modern sector becomes more productive, and the r2 -curve shifts upward. The A-equilibrium is unaltered because there is no modern sector in it. The B-equilibrium exhibits a higher equilibrium salary r = r1 = r2 . (See Figure 3a.) This is because the higher productivity of the modern sector implies that it can sustain a higher salary. As θ increases, the traditional sector is more productive. The r1 -curve shifts upward. The A-equilibrium implies a higher salary r, while the salary in the Bequilibrium drops. (Figure 3b) The increase of r in the A-equilibrium follows from the higher productivity of the traditional sector. The drop in the B-equilibrium occurs because as the traditional sector becomes more productive, more skilled workers move to it. This reduces the productivity of the modern sector (because of the reduced externalities), which sets a lower threshold for the pay of the skilled workers in the whole economy. [FIGURE 3 ABOUT HERE] Finally, if the supply of skilled workers k increases, the r1 -curve shifts downward, while the r2 -curve shifts upward. The downward movement of the r1 -curve follows from the standard characteristic of a constant-return-to-scale production that the productivity of any type of worker drops as a larger supply of that type of workers is available. The upward movement of the r2 -curve follows from the fact that the externalities in the modern sector imply a higher productivity of these firms as more skilled workers (and hence more potential firms or entrepreneurs) are available. The

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combined movement of the two curves (shown in Figure 3c) reduces the equilibrium salary in the A-equilibrium because the skilled workers are less scarce. The equilibrium salary increases in the B-equilibrium, as the potentially higher number of new firms reduces the average cost of production of each firm in the modern sector. Fewer skilled workers are then needed to produce any given quantity of the innovation, which makes the skilled workers more productive. In turn, this implies that the B-equilibrium can sustain higher salaries. n Case 2: The r2 -curve lies entirely below the r1 -curve The only other possibility in our economy is that the r2 -curve lies entirely below the r1 curve. In this case, r1 > r2 , ∀ h ∈ (0, 1]. As a result, only the A-equilibrium exists. The discussion above about the effects of changes in µ, θ, or k, also suggests that the r2 curve can lay entirely below the r1 -curve if µ or k are particularly small, or if θ is particularly high. That is, the modern sector does not arise if either one of the following conditions apply: i)

the modern sector is not very productive or demand is limited (χ or d);

ii)

the probability of success of the innovations q is low;

iii)

the individuals in the economy are too risk averse (high ρ), which may follow from the fact that the financial institutions for smoothing the innovation risks (e.g. venture capital) are not very advanced;

iv)

there is a limited supply of skilled people, which means that there cannot be enough new firms to produce the required externalities for the modern sector to rise;

v)

the productivity of the traditional sector is high, which increases the opportunity cost of the skilled workers to depart from that sector.

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The following Proposition summarises the whole discussion in this Section about the equilibrium allocations of our economy. Proposition 1 For µ or k sufficiently large, or θ sufficiently small, our economy has two stable equilibria, one with h = 1 (the A-equilibrium) and the other with h < 1 (the Bequilibrium). The equilibrium salary r is higher in the B-equilibrium vis-à-vis the Aequilibrium. If µ or k are sufficiently small or θ sufficiently large, only the Aequilibrium exists, and the modern sector will never arise.

4. INEQUALITY 4.1 Between Inequality In the previous section we have shown that rµA = 0; rθA > 0; rkA < 0 rµB > 0; rθB < 0; rkB > 0 where superscripts denote the equilibrium salary in the A- or B-equilibrium, and subscripts to denote first derivatives. Also, we have shown that in the B-equilibrium, hµ< 0, hθ > 0, and hk < 0. In this section we compare the wages of the unskilled workers, w, and the ratio between the salaries of the skilled workers and the wages of the unskilled workers, z≡

r , under the two equilibria. We take the latter to be our measure of inequality. We w

also study the effects of µ, θ, and k on w and z.

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The expression for w is simply (2) with h = 1 if we are in the A-equilibrium, and h < 1 if we are in the B-equilibrium. Similarly, our measure of inequality z is expression (3) with h= 1 or h < 1. The following Proposition then follows. Proposition 2 Other things being equal, the wage of the unskilled workers is higher in the Aequilibrium, wA > wB, and inequality is higher in the B-equilibrium, zB > zA. Since rB > rA, this Proposition says that the B-equilibrium is relatively better for the skilled workers, while the A-equilibrium favours the unskilled workers. The patterns of inequality are then profoundly different under the two equilibria. The reason why the unskilled workers are worse off in the B-equilibrium is that the lower supply of skilled workers in the traditional sector reduces their productivity, and hence their wages. As far as the effects of µ, θ, or k are concerned, we have to take into account that in the B-equilibrium h varies with these parameters. Moreover, in the Appendix we show that in the B-equilibrium,

∂ (h ⋅ k ) < 0 . From (2) and (3), it is then easy to see that ∂k

wµA = 0; wθA > 0; w kA > 0 wµB < 0; wθB > 0; wkB < 0 and z µA = 0; zθA > 0; z kA < 0 z µB > 0; zθB < 0; z kB > 0

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The same parameter changes can have opposite effects on the salaries of the skilled workers, the wages of the unskilled workers, and inequality under the two equilibria. 6 Consider first the effects of θ. This is the measure of skill-biased technical change typically used by the literature. Increases in θ do raise inequality, as suggested by the literature. In the A-equilibrium they increase both r and w, with the increase in r being more pronounced than the increase in w. This is different from the inequality produced by increases in µ in the B-equilibrium, in which r increases and w declines. The parameter µ is another form of skill-biased technical change. However, it is associated with a different organisational environment characterised by greater segregation of workers by skills (e.g. Kremer and Maskin, 1999; see also Acemoglu, 1999 and 2001.) Here the skilled workers become more productive in sectors where there is no complementarity with the unskilled workers; and this implies inequality wherein the wages of the unskilled workers decline. The supply of skills k also has opposite effects in the two equilibria. In the Aequilibrium, as noted earlier, greater k implies that the skilled workers are relatively less scarce compared to the unskilled workers. Hence, market forces reduce the relative salary of the former. By contrast, in the B-equilibrium, a greater k implies greater opportunities to exploit the knowledge externalities in the modern sector. This makes the skilled workers operating in that sector more productive, which encourages more skilled workers to join that sector. The reduced supply of skilled workers in the traditional sector then reduces the productivity of the unskilled workers.

6

The only derivatives which is not straight forward from inspecting (3) is z θB < 0 . This however follows

immediately from the fact that rθB < 0 and that wθB > 0 .

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4.2 The Demand for Skills The relative demand for skilled workers of this economy is depicted in Figure 4, where we draw z against k. We have shown that z kA < 0 and z kB > 0 . We have also seen that as k declines the r2 -curve will eventually lay entirely below the r1 -curve in Figure 2. As a result, there is a threshold k o such that for k > k o the demand for skills splits into two branches, one that is upward sloping and corresponds to the B-equilibrium, and the other one that is downward sloping and corresponds to the A-equilibrium. Any vertical supply curve of skills will then intersect the demand for skills twice denoting the two equilibria. For k < ko only the downward sloping portion of the demand curve exists, and any vertical vertical supply curve will intersect the demand for skills only once. [FIGURE 4 ABOUT HERE] Figure 4 also shows the effects of changes in µ or θ. Increases in µ shift up the rising portion of the demand curve. This is because for any given k, we have that z µB > 0 . They also reduce the threshold k o after which the B-equilibrium becomes possible. This is because at k = ko , where the r1 - and r2 -curves in Figure 2 are tangent to each other, increases in µ will shift the r2 -curve upward. A lower k is then needed to shift the r2 -curve back and the r1 -curve upward, and obtain tangency between the two curves again. Increases in θ shift the downward sloping portion of the demand curve up, and its rising portion down, as implied by zθA > 0 and zθB < 0 . They also move the threshold k o to the right. By the same reasoning as above, increases in θ must be offset by increases in k to make the r2 -curve intersect the r1 -curve.

19

4.3 Within Inequality Inequality between skills is typically accompanied by greater inequality “within” skills. Existing explanations of within skill inequality focus on differences in the ability of the individuals (Galor and Moav, 2000). Our model suggests another potential explanation. Within skill inequality could be associated with the expansion of jobs in which the incomes of the individuals depend on uncertain outcomes. We have labeled this phenomenon as “entrepreneurship” in this paper. As the opportunities in the modern sector rise, a greater number of people will become entrepreneurs, by which we mean that their income will be realised with probability q. The pattern however can be related to some broader changes in the nature of employment. Job mobility, risk-sharing employment contracts, and more generally jobs whose rewards are linked to performance, have become increasingly common, especially for the younger generations and for the more educated people. In the B-equilibrium, the structure of incomes of the skilled people is 1  − 1− ρ r ⋅ q   r  0  

k ⋅ ϕ ⋅ (1 − h) 1+ k k K−N= ⋅ (1 − ϕ ⋅ (1 − h)) 1+ k k (1 − q ) ⋅ N = (1 − q) ⋅ ⋅ ϕ ⋅ (1 − h) 1+ k q⋅N = q⋅

where the column on the left indicates the incomes, and the column on the right indicates the number of people who earn that income. Suppose that the profitability of the modern sector increases (either d or -χ increase). Because of the specific assumption about the utility of income in our paper, the ratio of high to middle income, −

q

1 1− ρ

, is unaffected. However, this raises the number of entrepreneurs N, as shown by

20

the fact that h decreases (because hµ < 0), and that ϕ is independent of d and χ. As a result, there will be a greater spread of incomes, with a larger fraction of skilled people earning either the high or the low income. Increases in the supply of skilled people will produce a similar increase in spread.

It is easy to see that -q⋅ϕ⋅hk >0, ϕ⋅hk < 0, and

(1-q)⋅ϕ⋅hk > 0, viz. the share of high and low income workers on the total number of skilled workers increase with k, while the share of middle income skilled workers decrease. Variations in the degree of risk aversion also affect within inequality. Here the implications are ambiguous. An economy with lower risk aversion (smaller ρ) will −

exhibit a lower ratio of high to mid-income q

1 1− ρ

. This is natural as lower risk aversion

means that the entrepreneurs require a lower expected income to set-up their firms. But the number of entrepreneurs also increase, as shown by ϕρ < 0, and hρ ≡ hµ⋅µρ > 0. We then have a more compressed structure of the salaries, but a higher share of people who earn the uncertain income. It is interesting to note that it is when risk aversion is high that we have the highest inequality in incomes. Venture capitalists or other institutions that help reduce the risk borne by the new entrepreneurs then also help reduce the inequality gap in incomes. It is when some individuals take some really big risk (possibly in a situation in which there are no advanced institutions for helping bear such a risk) that few successful will earn quite high incomes compared to the average population.

4.4 The Case with No Externalities In our model, the assumption of knowledge spillovers is not crucial for the modern sector to arise. It is however crucial for obtaining the two equilibria.

21

No spillovers means γ = 0. Hence, from (9) r2 = µ, and it is independent of h and k. Instead of a downward sloping curve for r2 as in Figure 2, we would have a flat curve. A graphical representation like the one in Figure 2 would easily show that we can have either µ < r 1 , or µ> r 1 . In the former case, the r2 -curve will be entirely below the r1 -curve, and only the A-equilibrium exists, while in the latter case the r2 -curve will be entirely above the r1 -curve, and only the B-equilibrium exists. The externalities implied by the nature of knowledge as an asset are then not crucial to explain the different patterns of inequality in the A- or B-equilibrium. But they are crucial to explain potential differences across countries in such patterns.

5. AVERAGE INCOME Average income in the A-equilibrium is y A = r A ⋅ K + w A ⋅ (1 − K ) . To write the average income yB in the B-equilibrium, recall that (K-N) skilled workers earn rB, q⋅N earn r ⋅ q B

−

1 1− ρ

, and the other skilled workers earn zero. This yields

y = r (K − N) + r q B

B

B

−

1 1− ρ

⋅ q ⋅ N + w B (1 − K ) .

By using the fact that N = ϕ⋅K⋅(1-h), we can then write k 1 ⋅ [1 + φ(1 − h) ] + w B ⋅ 1+ k 1+ k

yB = r B ⋅

where φ ≡

ε ⋅ (1 − q

−

1 1− ρ

1 − ε ⋅ (1 − q

−

)

= ϕ ⋅ (q

1 1− ρ

−

1 1- ρ

− 1) , and we used K ≡

)

(10)

k . The signs of the 1+ k

following derivatives are easy to establish: φρ > 0; φq < 0; ϕρ < 0; ϕq > 0.

22

It is not difficult to see that there is no inherent superiority of one or the other equilibrium in terms of average income. We then look at how the average incomes under the two equilibria change as µ, θ, or k change. n Changes in µ Since rA and wA are not affected by µ, yA is also unaffected by µ. To examine the effects of changes in µ on yB, we distinguish between variations in the profitability of the modern sector, d or -χ, and changes in the degree of risk aversion ρ. Changes in d or -χ have the same sign of the derivative of yB with respect to µ, i.e. y µB . To compute this derivative from (10), we take into account that hµ < 0, and by taking the derivatives of rB and wB with respect to µ from (1) and (2), one can show that wµB = −rµB ⋅ (hk ) . Since r Bk r > 0 , this yields y = 1+ k B µ

B µ

 rµB   B (1 − h)(1 + φ) − φ ⋅ hµ  > 0 . That is, increases in d or  r 

in -χ make the B-equilibrium more attractive in terms of average income of the economy. To establish the effect of risk aversion on yB, we also need to take into account that ρ directly affects φ in (10). Hence, to obtain the expression for y ρB , one needs to multiply y µB by µρ < 0, and add the extra term φρ⋅(1-h). This yields y ρB = y µB ⋅ µρ + φρ ⋅ (1 − h) . Since φρ > 0, the two terms of this expression have opposite signs. However, we show in the Appendix that the first term dominates, and therefore an economy with lower risk aversion has a higher average income in the B-equilibrium. The intuition is that with a lower degree of risk aversion, the entrepreneurs demand a −

lower expected premium q

ρ 1− ρ

to become entrepreneurs. More new firms will be

23

formed, and the productivity of the modern sector rises because of the wider spillovers. This is an interesting result, as it links the observed reduction in technological risk produced by institutions like venture capital or else in several high-tech industries, and the corresponding formation of high-tech start-ups, with both increases in the average income of the economy and in the inequality both between and within skills. n Changes in θ Since both rA and wA increase with θ, then yA increases with θ. To compute yθB from (10) we use hθ > 0, and the fact that given the expressions for the derivatives rθB and  rB  wθB from (1) and (2), wθB = r ⋅ ( hk ) ⋅  θ −1 − θB  . The sign of yθB is then equal to the r   sign of the following expression 2 rθB h  θ ⋅ hθ  σ − 1   (1 + φ) ⋅ (1 − h ) − φ ⋅ −   r θ  h  σ  

Since rθB < 0 , a sufficient condition for yθB < 0 is that the expression in the square brackets be non-negative. From (3) one obtains z = (θ ⋅ hk ) B θ

Since zθB < 0 , it must be that

−

1 σ

 σ − 1 θ hθ  ⋅ − ⋅ . σ h  σ

θ ⋅ hθ θ ⋅ hθ > σ − 1 , and if we replace σ − 1 for inside h h

the square brackets, we obtain a minimum for that expression. As a result, a sufficient condition for the sign of the expression inside the square brackets to be positive is that φ − σ − 1  > 0 . This will obtain if φ is sufficiently large. A large φ obtains whenever  σ 2  q

ρ 1− ρ

is small, which in turn corresponds to a small share of entrepreneurs ϕ.

24

Thus, when the conditions of the economy are such that in a B-equilibrium there are few entrepreneurs (e.g. small probability of success q, or high risk aversion), then if the economy also features a large θ, it is likely that its average income in the Bequilibrium be smaller than that in the A-equilibrium. As we shall also discuss in the next section, this is suggestive for instance of why advanced economies with technologically sophisticated large firms and traditional industries are less likely to give rise to the modern sector, and they are less likely to produce the implied inequality across skills. n Changes in k In the A-equilibrium there is an optimal supply of k which maximises yA. It can be easily shown that this is k * = θ σ −1 . Moreover, the optimal yA is obtained when rA = wA, viz. when the rents from being a skilled worker have been completely exhausted. To compute y kB we use the fact that hk < 0, and that wkB = −rkB ⋅ (hk ) , which is derived from (1) and (2). From (10), one can show that a sufficient condition for y kB > 0 is that the following expression be positive  wB  φ ⋅ (1 − h) − φ ⋅ hk ⋅ k + (1 − r B )    Suppose that the economy is in its long-run A-equilibrium with rA = wA, and that the Bequilibrium also exists. In the A-equilibrium, further increases in the supply of skills k will reduce the average income. Other things being equal we know that rB>rA, and wB 0 , which implies hk < 0.) After ∂h ∂h ∂k ∂k some algebra one finds that hk ⋅k + h < 0. (The same strategy − viz. differentiation of the equilibrium condition r1 = r2 with respect to h and µ or θ − will produce the expressions for h µ or hθ.) QED

Claim The average income in a B-equilibrium decreases with increases in risk aversion, viz. y ρB = y µB ⋅ µρ + φρ ⋅ (1 − h) < 0 .

31

Proof Given the expression for µ, one obtains µρ =

φρ = −

[

]

log( q ) ε + γ ⋅ (1 − ε) 2 ⋅ (1 + φ) . Also, 2 (1 − ρ)

ρ 1− ρ

ε⋅ q log( q ) ⋅ , which implies 2 (1 + φ) (1 − ρ) 2

[

φρ ⋅ µ

]

µρ = − ε + γ ⋅ (1 − ε) 2 ⋅ (1 + φ) ⋅

ρ

ε ⋅q

1− ρ

(1 + φ) 2

Replace this expression and the expression for φρ in y ρB = y µB ⋅ µρ + φρ ⋅ (1 − h) . As rB k noted in the text, y = 1+ k B µ

 rµB   B (1 − h )(1 + φ) − φ ⋅ hµ  . The expression for hµ is derived  r 

from differentiating the equilibrium condition r1 = r2 , as indicated in the previous claim. This also produces the expression for rµB , which depends on hµ. After some algebra, the postive term φρ ⋅ (1 − h) in the expression for y ρB is netted out. Hence, y ρB < 0 . QED

References Acemoglu, D. (2001) “Technical Change, Inequality, and the Labor Market”, Journal of Economic Literature, forthcoming. Acemoglu, D. (1999) “Changes in Unemployment and Wage Inequality: An Alternative Theory and Some Evidence” American Economic Review, Vol.89, 1259-1278. Aghion, P., Caroli, E. and Garcia-Peñalosa (1999) “Inequality and Economic Growth: The Perspective of the New Growth Theories”, Journal of Economic Literature, Vol.37 (4), 1615-1660. Arora, A., Arunachalam, V.S., Asundi, J., and Fernandes, R. (2001) “The Indian Software Services Industry”, Research Policy, Vol. 30 (8), 1267-1287.

32

Arora, A., Fosfuri, A., and Gambardella, A. (2001) Markets for Technology: The Economics of Innovation and Corporate Strategy, MIT Press, Cambridge MA. Arora, A., Gambardella, A., and Torrisi, S. (2001) “In the Footsteps of Silicon Valley? The Software Industry in India and Ireland and the International Division of Labour”, mimeo, Carnegie Mellon University, Pittsburgh PA. Baldwin, C. and Clark, K. (1997) “Managing in an Age of Modularity”, Harvard Business Review, Vol.75(5), 84-93. Berman, E., Bound, J., and Machin, S. (1998) “Implications of Skill Biased Technological Change: International Evidence”, Quarterly Journal of Economics, Vol. CXIII (4), 1245-1279. Bernard, A. and Bradford Jensen, J. (1998) “Understanding Increasing and Decreasing Wage Inequality”, NBER Working Paper N.6571, NBER, Cambridge MA. Bresnahan, T. (1999) “Computerisation and Wage Dispersion: An Analytical Reinterpretation”, Economic Journal, Vol.109, F390-F415. Bresnahan, T., Brynjolfsson, E. and Hitt, L. (2001) “Information Technology, Workplace Organization and the Demand for Skilled Labour: Firm-level Evidence”, Quarterly Journal of Economics, forthcoming. Caroli, E. and Van Reenen, J. (2001) “Skill Biased Organizational Change? Evidence from a Panel of British and French Establishment”, Quarterly Journal of Economics, Vol. CXVI (4), 1442-1492. Casavola, P., Gavosto, A., and Sestito, P. (1996) “Technical Progress and Wage Dispersion in Italy: Evidence from Firms’ Data”, Annales d’Economie et de Statistique, N.41/42, 387-412. Chandler, A. (1990) Scale and Scope. The Dynamics of Industrial Capitalism, The Belknap Press of Harvard University Press, Cambridge MA. Chesbrough, H. (1999) “The Organizational Impact of Technological Change: A Comparative Theory of National Institutional Factors”, Industrial and Corporate Change, Vol.8 (3), 447-485. Chesbrough, H. (2000) “Designing Corporate Ventures in the Shadow of Private Venture Capital”, California Management Review 42 (3), 31-49. The Economist (1999) “Innovation in Industry”, Special Survey, Febr.20, pp.1-28. Feldstein, M. (1998) “Income Inequality and Poverty”, NBER Working Paper N.6770, Cambridge MA.

33

Galor, O. Moav, O. (2000) “Ability Biased Technological Transition, Wage Inequality and Economic Growth”, Quarterly Journal of Economics, Vol. CXV, 469498. Goldin, C. and Katz, L. (1998) “The Origins of Technology-Skill Complementarity”, Quarterly Journal of Economics, Vol. CXIII, 693-732. Gottschalk, P. (1997) “Inequality, Income Growth, and Mobility: The Basic Facts”, Journal of Economic Perspectives, Vol.11 (2), 21-40. Gottschalk, P. and Smeeding, T. (1997) “Cross-National Comparisons of Earnings and Income Inequality”, Journal of Economic Literature, Vol. XXXV (2), 633-681. Hall, B.H. and Ham, R. (2001) “The Patent Paradox Revisited: Determinants of Patenting in the US Semiconductor Industry, 1980-1994”, RAND Journal of Economics 32 (1), 101-128. Juhn, C., Murphy, K., and Pierce, B. (1993) “Wage Inequality and the Rise in Returns to Skill”, Journal of Political Economy, Vol. 101 (3), 410-442. Kremer, M. and Maskin, E. (1999) “Segregation By Skill and the Rise in Inequality”, mimeo, Department in Economics, Harvard University, Cambridge MA. Langlois, R. and Robertson, P. (1992) “Networks and Innovation in a Modular System: Lessons from the Microcomputer and Stereo Component Industries”, Research Policy, Vol.21, 297-313. Levinthal, D. and March, J. (1993) “The Myopia of Learning”, Strategic Management Journal, Vol.14, 95-112. Macher, J., Mowery, D., and Hodges, D. (1999) “Semiconductors”, in Mowery, D. (ed.), US Industry in 2000: Studies in Competitive Performance, National Academy Press, Washington DC. Machin, S. and Van Reenen, J. (1998) “Technology and Changes in Skill Structure: Evidence from Seven OECD Countries”, Quarterly Journal of Economics, Vol. CXIII (4), 1215-1244. Saxenian, A. (1994) Regional Advantage, Harvard University Press, Cambridge MA.

34

FIGURE 1: S EQUENCE OF ALLOCATIONS AND PAY-OFFS

w 1-K r1 H1

ð   0

K

N

q 1−q

H2

H2 - N r2

FIGURE 2: THE A- AND B-EQUILIBRIA r1 , r2

r2

B r2

r1 C

r1

hC

35

A

1

h

FIGURE 3: COMPARATIVE STATICS OF CHANGES IN µ, θ, OR k r1 , r2 B’ B Figure 3a: Increases in µ

A h

r1 , r2

B Figure 3b: Increases in θ

B’

A’ A h

r1 , r2 B’ B

Figure 3c: Increases in k A A’ h

36

FIGURE 4: THE D EMAND FOR SKILLS z higher θ B higher µ

A’ higher θ A k

ko

FIGURE 5: INDEXED WAGES OF WHITE M ALES IN THE US, 1963-1997 (1963=100)

Years

Source: Acemoglu (2001)

37

TABLE 1: LABOUR COST COMPARISONS IN THE SOFTWARE INDUSTRY (ANNUAL LABOUR COST IN 1995 US $)

USA

Ireland

India

Project Leader (A)

54000

43000

23000

Systems Analyst (B)

48000

36000

14000

Development Programmer (C)

41000

21000

8000

Support Programmer (D)

37000

21000

8000

Network Analyst/ Designer

49000

26000

14000

Quality Assurance Specialist

50000

29000

14000

Test Engineer

47000

na

8000

(A)/(C)

1.32

1.55

2.18

(A)/(D)

1.46

1.40

1.97

(B)/(C)

1.17

1.46

1.50

(B)/(D)

1.30

1.32

1.35

Source: Arora, Gambardella, and Torrisi (2001)

38